On the two-step method for solving nonlinear equations with nondifferentiable operator

We study a local and a semilocal convergence of the two-step method for solving nonlinear equations with a nondifferentiable operator. Its method is based on two methods of order of convergence . We carry out the numerical research on test problems and do the comparison of obtained results. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On an one-step modification of Gauss-Newton method under generalized Lipschitz conditions for solving the nonlinear least squares problem

We investigate convergence of the one-step modification of Gauss-Newton method using the divided differences and the weak generalized Lipschitz condition for the divided differences. Convergence order of the method was examined and the uniqueness ball for the solution of the nonlinear least squares problem was proved. Numerical experiments were also provided. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Universality hypothesis for the small wave-number range of decaying turbulence

In the frame of a model of the decaying, locally homogeneous isotropically developed turbulence the energy spectrum is investigated in energy-containing range. The self-similar solution of energy spectral balance equation has been found.This work was supported by the Slovak Grant Agency for Science (grant No. 2/550/93), by the Fundamental Research Russian Fund and by the International Scientific Fund (grant No. R-63000).     

Direct palladium-catalyzed arylation of cyclopropenes

The first examples of direct palladium-catalyzed arylation and heteroarylation of cyclopropenes have been demonstrated. This method allows for efficient synthesis of various tetrasubstituted cyclopropenes, incuding nonracemic cyclopropenes, which are not available via known asymmetric cyclopropenation methods. Mechanistic studies strongly suggest an electrophilic path for this Heck-type transformation.     

Gas chromatography-mass spectrometry analysis of alkylphenols in produced water from offshore oil installations as pentafluorobenzoate derivatives

A simple, highly selective and sensitive method for the determination of 14 representative alkylphenols from phenol (C0) to nonylphenol (C9) in produced water is described. Solid-phase extraction (SPE) by anion-exchange sorbent is used to extract alkylphenols from produced water. The samples are then derivatised by pentafluorobenzoyl chloride and analysed on GC-MS (negative ion chemical ionisation, NCI). The derivatisation procedure has been validated by means of two-level factorial design (2(7-4)) experiments. Quantification is done with isotope dilution of five internal standards of different alkyl chain length. The detection limits were at low ng/l levels. A comparison with GC-MS analysis of non-derivatised alkylphenol samples revealed the advantage of derivatisation as described in the method.     

Untersuchungen über den Infektionsverlauf von Tabakmosaikvirus in nicotiana tabacum mit Hilfe von14C-markiertem Virus

Zusammenfassung Es wurde¹⁴C-markiertes Tabakmosaikvirus (TMV) von hoher spezifischer Aktivität durch Radiophotosynthese hergestellt und damit nicotiana tabacum-Pflanzen beimpft. Zu drei verschiedenen Zeiten nach derTMV-Beimpfung wurden die Pflanzen geerntet und das primär infizierte Blatt jeweils getrennt von der übrigen Pflanze aufgearbeitet. Neben demTMV wurden noch die Chloroplasten, die pH 4,7- und pH 3,0-Fraktion, die pufferunlöslichen Fraktionen und die niedermolekularen Zellbestandteile isoliert. Aus dem Verhältnis der Aktivitätswerte Protein zu Nukleinsäure (NS) kann man annehmen, daß die Virus-Ribonukleinsäure (RNS) allein oder zumindestens zum überwiegenden Teil ohne ihren Proteinmantel in die systemisch infizierten Teile der Pflanze wandert und daß der Proteinanteil zum Großteil an pufferunlösliche Zellbestandteile gebunden bleibt.Aus dem Institut für Biologie und Landwirtschaft des Reaktorzentrums Seibersdorf (Leiter: Doz. Dr.K. Kaindl)     

Photopolymerization of water-soluble acrylic monomers induced by colloidal CdS and Cd x Zn1 − x S nanoparticles

Photocatalytic activity of CdS and Cd _x Zn_1−x S nanoparticles in the polymerization of acrylamide and acrylic acid in aqueous solutions has been found. It has been shown that the most probable way of the photogeneration of primary radicals is the reduction of an adsorbed monomer by the conduction band electrons of the semiconductor nanoparticles, a monomer oxidation by the valence band holes and atomic hydrogen addition to a monomer being complementary photoinitiation routes. A correlation between the composition of Cd_xZn_1-xS nanoparticles and their photocatalytic activity in the acrylamide polymerization has been established. It has been shown that an increase in the quantum yield of the photopolymerization in a sequence СdS < Cd_0.75Zn_0.25S < CdS_0.5Zn_0.5S < Cd_0.3Zn_0.7S originates from a concurrent increase of the conduction band potential of the semiconductor nanoparticles. A kinetic equation of the photocatalytic acrylamide polymerization has been derived. Quantum yields of the photoinitiation have been found to be as small as 10⁻⁴ to 10⁻³.